Question

Clarification question:

If I have a plane like 2x+5y-z = 6, does this mean that (2,5,-1) represents a vector parallel to the plane or orthogonal to the plane?

Answer 1

I think its the orthogonal because the Cartesian equal of a plane in R^3 is Ax+By+Cz+D=0, where vector n=(A,B,C) is a normal to the plane...

Answer 2

Exactly. Which is what I thought, but something came up that made me question that and I had to be sure.

Answer 3

what' the question that came up in your mind? maybe I'm wrong..

Answer 4

I had a problem solved where they took what I thought was the normal vector to the plane and found a vector that made a dot productof 0 with that vector. Which made me think, if you make a 0 dot product with something that is orthogonal, doesn't that make it parallel? So it seemed like it was the opposite to whatI wanted. It just made mequestion why they found a vector that formed a dot product of 0 with the normal vector xD

Answer 5

lol, i think my head will explode if I think that much! O_0

Answer 6

Doesnt help Im playing chess while I do this.

Answer 7

you can do things at a time?

Answer 8

Not at the SAME time, lol. But I have to keep busy somehow.

Answer 9

calculus one?

Answer 10

3

Answer 11

Beginning of it.